338 lines
9.5 KiB
Common Lisp
338 lines
9.5 KiB
Common Lisp
;;; WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD
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;;; WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD
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;;; WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD WHITEHEAD
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(IN-PACKAGE "CAT")
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(provide "whitehead")
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;;;
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;;; Z
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;;;
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(DEFUN Z-WWHITEHEAD-SINTR (smst n chml-clss
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&aux (face (face smst))
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(k-z-n (k-z n))
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(idnt (bsgn k-z-n))
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(efhm (efhm smst)))
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(declare
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(type simplicial-set smst)
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(fixnum n)
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(type morphism chml-clss)
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(type face face)
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(type ab-simplicial-group k-z-n)
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(type gmsm idnt)
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(type equivalence efhm))
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(setf chml-clss
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(i-cmps chml-clss (rf efhm) (lg efhm)))
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(flet ((rslt (dmns gmsm)
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(declare
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(fixnum dmns)
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(type gmsm gmsm))
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(if (< dmns n)
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(absm (mask dmns) idnt)
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(z-cocycle-gbar n dmns
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(gmsm-cocycle face n dmns gmsm chml-clss)))))
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(the sintr #'rslt)))
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#|
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(cat-init)
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(setf k (k-z 2))
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(setf ecc (echcm k))
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(setf chml-clss
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(morphism
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:sorc ecc :trgt (z-chcm) :degr 2
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:intr #'(lambda (degr gnrt)
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(if (= degr 2)
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(term-cmbn 0 1 :z-gnrt)
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(zero-cmbn (- degr 2))))
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:strt :gnrt :dfnt '(fundamental-class k-z-2)))
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(setf tw (z-wwhitehead-sintr k 2 chml-clss))
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(a-sintr3 tw 1 (absm 1 +null-gbar+))
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(a-sintr3 tw 2 (absm 3 +null-gbar+))
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(funcall tw 2 (gbar 2 0 '(55) 0 '()))
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(funcall tw 3 (gbar 3 0 '(12 23)
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0 '(34)
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0 '()))
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(funcall tw 4 (gbar 4 0 '(12 23 34)
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2 '(45)
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0 '(56)
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0 '()))
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(setf k (k-z 3))
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(setf ecc (echcm k))
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(setf chml-clss
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(morphism
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:sorc ecc :trgt (z-chcm) :degr 3
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:intr #'(lambda (degr gnrt)
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(if (= degr 3)
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(term-cmbn 0 -1 :z-gnrt)
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(zero-cmbn (- degr 3))))
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:strt :gnrt :dfnt '(fundamental-class k-z-3)))
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(setf tw (z-wwhitehead-sintr k 3 chml-clss))
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(a-sintr3 tw 1 (absm 1 +null-gbar+))
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(a-sintr3 tw 2 (absm 3 +null-gbar+))
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(a-sintr3 tw 3 (absm 7 +null-gbar+))
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(funcall tw 3 (z-fundamental-gmsm 3 55))
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(equal (funcall tw 3 (z-fundamental-gmsm 3 55))
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(absm 0 (z-fundamental-gmsm 3 55)))
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(funcall tw 4 (gbar 4 0 (gbar 3 0 '(12 23) 0 '(34) 0 '())
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0 (gbar 2 0 '(45) 0 '())
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1 (gbar 0)
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0 (gbar 0)))
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|#
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(DEFUN Z-WHITEHEAD-SINTR (smst n chml-clss
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&aux (face (face smst))
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(k-z-n-1 (k-z (1- n)))
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(idnt (bsgn k-z-n-1))
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(efhm (efhm smst)))
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(declare
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(type simplicial-set smst)
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(fixnum n)
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(type morphism chml-clss)
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(type face face)
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(type ab-simplicial-group k-z-n-1)
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(type gmsm idnt)
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(type equivalence efhm))
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(setf chml-clss
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(i-cmps chml-clss (rf efhm) (lg efhm)))
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(flet ((rslt (dmns gmsm)
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(declare
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(fixnum dmns)
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(type gmsm gmsm))
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(if (< dmns n)
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(absm (mask (1- dmns)) idnt)
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(z-cocycle-gbar-head n dmns
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(gmsm-cocycle face n dmns gmsm chml-clss)))))
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(the sintr #'rslt)))
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#|
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(cat-init)
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(setf k (k-z 2))
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(setf ecc (echcm k))
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(setf chml-clss
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(morphism
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:sorc ecc :trgt (z-chcm) :degr 2
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:intr #'(lambda (degr gnrt)
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(if (= degr 2)
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(term-cmbn 0 1 :z-gnrt)
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(zero-cmbn (- degr 2))))
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:strt :gnrt :dfnt '(fundamental-class k-z-2)))
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(setf tw (z-whitehead-sintr k 2 chml-clss))
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(tw-a-sintr3 tw 1 (absm 1 +null-gbar+) '())
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(tw-a-sintr3 tw 2 (absm 3 +null-gbar+) '())
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(funcall tw 2 (gbar 2 0 '(55) 0 '()))
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(funcall tw 3 (gbar 3 0 '(12 23)
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0 '(34)
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0 '()))
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(funcall tw 4 (gbar 4 0 '(12 23 34)
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2 '(45)
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0 '(56)
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0 '()))
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(setf k (k-z 3))
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(setf ecc (echcm k))
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(setf chml-clss
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(morphism
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:sorc ecc :trgt (z-chcm) :degr 3
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:intr #'(lambda (degr gnrt)
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(if (= degr 3)
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(term-cmbn 0 -1 :z-gnrt)
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(zero-cmbn (- degr 3))))
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:strt :gnrt :dfnt '(fundamental-class k-z-3)))
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(setf tw (z-whitehead-sintr k 3 chml-clss))
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(tw-a-sintr3 tw 1 (absm 1 +null-gbar+) +null-gbar+)
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(tw-a-sintr3 tw 2 (absm 3 +null-gbar+) +null-gbar+)
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(tw-a-sintr3 tw 3 (absm 7 +null-gbar+) +null-gbar+)
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(funcall tw 3 (z-fundamental-gmsm 3 55))
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(equal (funcall tw 3 (z-fundamental-gmsm 3 55))
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(absm 0 (z-fundamental-gmsm 2 55)))
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(funcall tw 4 (gbar 4 0 (gbar 3 0 '(12 23) 0 '(34) 0 '())
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0 (gbar 2 0 '(45) 0 '())
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1 (gbar 0)
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0 (gbar 0)))
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|#
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(DEFUN Z-WHITEHEAD (smst chml-clss &aux (n (- (degr chml-clss))))
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(declare
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(type simplicial-set smst)
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(fixnum n)
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(type morphism chml-clss))
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(the fibration
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(simplicial-mrph
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:sorc smst :trgt (k-z (1- n)) :degr -1
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:sintr (z-whitehead-sintr smst n chml-clss)
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:dfnt `(z-whitehead ,smst))))
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;;;
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;;; Z/2Z
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;;;
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(DEFUN Z2-WWHITEHEAD-SINTR (smst n chml-clss
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&aux (face (face smst))
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(k-z2-n (k-z2 n))
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(idnt (bsgn k-z2-n))
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(efhm (efhm smst)))
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(declare
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(type simplicial-set smst)
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(fixnum n)
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(type morphism chml-clss)
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(type face face)
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(type ab-simplicial-group k-z2-n)
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(type gmsm idnt)
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(type equivalence efhm))
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(setf chml-clss
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(i-cmps chml-clss (rf efhm) (lg efhm)))
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(flet ((rslt (dmns gmsm)
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(declare
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(fixnum dmns)
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(type gmsm gmsm))
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(if (< dmns n)
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(absm (mask dmns) idnt)
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(z2-cocycle-gbar n dmns
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(gmsm-cocycle face n dmns gmsm chml-clss)))))
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(the sintr #'rslt)))
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#|
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(cat-init)
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(setf k (k-z2 2))
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(setf ecc (echcm k))
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(setf chml-clss
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(morphism
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:sorc ecc :trgt (z-chcm) :degr 2
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:intr #'(lambda (degr gnrt)
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(if (= degr 2)
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(term-cmbn 0 1 :z-gnrt)
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(zero-cmbn (- degr 2))))
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:strt :gnrt :dfnt '(fundamental-class k-z-2)))
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(setf tw (Z2-wwhitehead-sintr k 2 chml-clss))
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(a-sintr3 tw 1 (absm 1 +null-gbar+))
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(a-sintr3 tw 2 (absm 3 +null-gbar+))
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(funcall tw 2 (gbar 2 0 1 0 0))
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(funcall tw 3 (gbar 3 0 2
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0 1
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0 0))
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(funcall tw 4 (gbar 4 0 3
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2 1
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0 1
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0 0))
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(setf k (k-z2 3))
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(setf ecc (echcm k))
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(setf chml-clss
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(morphism
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:sorc ecc :trgt (z-chcm) :degr 3
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:intr #'(lambda (degr gnrt)
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(if (= degr 3)
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(term-cmbn 0 -1 :z-gnrt)
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(zero-cmbn (- degr 3))))
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:strt :gnrt :dfnt '(fundamental-class k-z-3)))
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(setf tw (Z2-wwhitehead-sintr k 3 chml-clss))
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(a-sintr3 tw 1 (absm 1 +null-gbar+))
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(a-sintr3 tw 2 (absm 3 +null-gbar+))
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(a-sintr3 tw 3 (absm 7 +null-gbar+))
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(funcall tw 3 (Z2-fundamental-gmsm 3 1))
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(equal (funcall tw 3 (Z2-fundamental-gmsm 3 1))
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(absm 0 (Z2-fundamental-gmsm 3 1)))
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(funcall tw 4 (gbar 4 0 (gbar 3 0 2 0 1 0 0)
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0 (gbar 2 0 1 0 0)
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1 (gbar 0)
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0 (gbar 0)))
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|#
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(DEFUN Z2-WHITEHEAD-SINTR (smst n chml-clss
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&aux (face (face smst))
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(k-z2-n-1 (k-z2 (1- n)))
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(idnt (bsgn k-z2-n-1))
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(efhm (efhm smst)))
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(declare
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(type simplicial-set smst)
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(fixnum n)
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(type morphism chml-clss)
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(type face face)
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(type ab-simplicial-group k-z2-n-1)
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(type gmsm idnt)
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(type equivalence efhm))
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(setf chml-clss
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(i-cmps chml-clss (rf efhm) (lg efhm)))
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(flet ((rslt (dmns gmsm)
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(declare
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(fixnum dmns)
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(type gmsm gmsm))
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(if (< dmns n)
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(absm (mask (1- dmns)) idnt)
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(z2-cocycle-gbar-head n dmns
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(gmsm-cocycle face n dmns gmsm chml-clss)))))
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(the sintr #'rslt)))
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#|
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(cat-init)
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(setf k (k-z2 2))
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(setf ecc (echcm k))
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(setf chml-clss
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(morphism
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:sorc ecc :trgt (z-chcm) :degr 2
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:intr #'(lambda (degr gnrt)
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(if (= degr 2)
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(term-cmbn 0 1 :z-gnrt)
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(zero-cmbn (- degr 2))))
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:strt :gnrt :dfnt '(fundamental-class k-z-2)))
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(setf tw (Z2-whitehead-sintr k 2 chml-clss))
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(tw-a-sintr3 tw 1 (absm 1 +null-gbar+) 0)
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(tw-a-sintr3 tw 2 (absm 3 +null-gbar+) 0)
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(funcall tw 2 (gbar 2 0 1 0 '()))
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(funcall tw 3 (gbar 3 0 2
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0 1
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0 0))
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(funcall tw 4 (gbar 4 0 3
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2 1
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0 1
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0 0))
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(setf k (k-z2 3))
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(setf ecc (echcm k))
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(setf chml-clss
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(morphism
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:sorc ecc :trgt (z-chcm) :degr 3
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:intr #'(lambda (degr gnrt)
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(if (= degr 3)
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(term-cmbn 0 -1 :z-gnrt)
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(zero-cmbn (- degr 3))))
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:strt :gnrt :dfnt '(fundamental-class k-z-3)))
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(setf tw (Z2-whitehead-sintr k 3 chml-clss))
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(tw-a-sintr3 tw 1 (absm 1 +null-gbar+) 0)
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(tw-a-sintr3 tw 2 (absm 3 +null-gbar+) 0)
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(tw-a-sintr3 tw 3 (absm 7 +null-gbar+) 0)
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(funcall tw 3 (Z2-fundamental-gmsm 3 1))
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(equal (funcall tw 3 (Z2-fundamental-gmsm 3 1))
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(absm 0 (Z2-fundamental-gmsm 2 1)))
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(funcall tw 4 (gbar 4 0 (gbar 3 0 2 0 1 0 0)
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0 (gbar 2 0 1 0 0)
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1 (gbar 0)
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0 (gbar 0)))
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|#
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(DEFUN Z2-WHITEHEAD (smst chml-clss &aux (n (- (degr chml-clss))))
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(declare
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(type simplicial-set smst)
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(fixnum n)
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(type morphism chml-clss))
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(the fibration
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(simplicial-mrph
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:sorc smst :trgt (k-z2 (1- n)) :degr -1
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:sintr (Z2-whitehead-sintr smst n chml-clss)
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:dfnt `(Z2-whitehead ,smst))))
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#|
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(setf m (moore 2 4))
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(setf chml-clss
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(morphism
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:sorc m :trgt (z-chcm) :degr -4
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:intr #'(lambda (dmns gmsm)
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(if (= 4 dmns)
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(cmbn 0 1 :z-gnrt)
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(zero-cmbn (- dmns 4))))
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:strt :gnrt
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:dfnt '(chml-clss moore 2 4)))
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(setf mf (z2-whitehead m 4 chml-clss))
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(setf mt (fibration-total mf))
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(homology mt 0 10)
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|#
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